Simplify; express your answer in exponential form. Assume $x\neq 0, a\neq 0$. $\dfrac{{(x^{-3})^{2}}}{{(x^{-1}a^{5})^{-3}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{-3}}$ to the exponent ${2}$ . Now ${-3 \times 2 = -6}$ , so ${(x^{-3})^{2} = x^{-6}}$ In the denominator, we can use the distributive property of exponents. ${(x^{-1}a^{5})^{-3} = (x^{-1})^{-3}(a^{5})^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(x^{-3})^{2}}}{{(x^{-1}a^{5})^{-3}}} = \dfrac{{x^{-6}}}{{x^{3}a^{-15}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{-6}}}{{x^{3}a^{-15}}} = \dfrac{{x^{-6}}}{{x^{3}}} \cdot \dfrac{{1}}{{a^{-15}}} = x^{{-6} - {3}} \cdot a^{- {(-15)}} = x^{-9}a^{15}$.